**Karl Heinrich Weise**was born in Gera, a town in Thüringen, Germany, on the Weisse Elster River about 55 km southwest of Leipzig. After completing his schooling at the Gymnasium, he studied at the university in Leipzig and then in Jena with Robert König as his thesis supervisor. In 1934 he was awarded his doctorate for his thesis

*Beiträge zum Klassenproblem der quadratischen Differentialformen*Ⓣ. He continued undertaking research at Jena and, in 1937, he got the Habilitation and became an Assistant and Privatdozent there. As an example of his work from this period we mention three papers he published in 1940: (with Robert König)

*Zur konformen Abbildung zweier Flächen mit beliebigen Parametern*Ⓣ;

*Bemerkung zur Abbildung zweier Flächen*Ⓣ; and

*Invariante Charakterisierung von Kurvennetzen*Ⓣ. On 1 November 1942 he was appointed 'planmässiger ausserordentlicher Professor' (associate professor with tenure) at the Christian Albrechts Universität in Kiel where he was promoted to a full professorship on 1 November 1945, becoming the successor of Adolf Hammerstein (1888-1941).

Due to World War II, lecturing had stopped in Kiel in 1943 as bombing raids intensified. During the bombing, the rooms of the 'Mathematisches Seminar' had been completely destroyed and so it was Weise's task to make a new start under extremely difficult circumstances. In fact the first courses were given on a ship that had survived the bombing. Later the university moved to a new campus ('Neue Universität', a name that often has led to misunderstandings) that was inherited from a military factory that, in contrast to the old main building of the university, also had survived the bombing. Together with Friedrich Bachmann, who was appointed to a second professorship of mathematics in 1948, he had the main share in rebuilding mathematics in Kiel after the war. Not only did he give vivid and inspiring lectures on many topics, in particular on analysis, but also he soon showed a particular talent for organisational tasks: for the year 1951-52 he was elected dean of the faculty of philosophy, and for the year 1952-53 rector of the university. One of his former students who went on to become a professor, Manfred Schimmler, commented on Weise's organisational skills [1]:-

Weise very early realized the potential of electronic computers for mathematics and in fact in 1957-58, together with the nuclear physicist Erich Bagge, he founded the computer centre of the university. Hans Langmaack, a professorial colleague at Kiel, said [1]:-He was the kind of manager who knew how to surround himself with the right people and from this the correct actions came about.

Although he had both experience and talent for numerical computations and lectured on many aspects of numerical mathematics, he also realized the possibility of doing non-numerical computations and so he insisted that Kiel would get flexible binary computers. Their first computer was a Z22 of Konrad Zuse, and later came the X1 and X8 of Electrologica. Weise himself, with an assistant, did computations on knot theory, Bodo Schender, one of his former students who was to become the first professor of computer science at Kiel, developed formula manipulation methods for trigonometric functions, and also the first steps in what is now known as 'Computational Group Theory' were undertaken as early as 1959 on the Z22. In 1971 Weise also founded a new 'Institut für Informatik und Praktische Mathematik' which became the nucleus of Computer Science at Kiel. He served as Director of the Institute from 1971 to 1977.He never taught computer science, but he was the visionary who saw how important this subject is.

Weise also lent his insight and organisational talent to a wide range of organisations furthering science in Germany. In 1955-56 he was elected chairman of the 'Deutsche Mathematiker-Vereinigung' (German mathematical society), from 1964 to 1970 he was a member of the 'Wissenschaftsrat', the central advisory body for the federal government on the development of science in Germany, and Chairman of the 'Wissenschaftliche Kommission'. He also served as 'Vertrauensdozent' (Local representative) of the Deutsche Forschungsgemeinschaft, as a member of the advisory committee on Computer Science of the federal ministry for research, and last but not least supported in many ways the development of the Oberwolfach Institute. In recognition of his services he was awarded the 'Bundesverdienstkreuz' (order of merit of the Federal Republic).

Weise's mathematical work was mainly on questions from differential geometry and topology. In 1951, jointly with Robert König, he published the book *Mathematische Grundlagen der Höheren Geodäsie und Kartographie* Ⓣ. N A Hall writes in a review:-

In years soon after the war Weise published a small but concise bookThe field of higher geodesy and cartography is one specialized branch of geometry and analysis which has been the subject of many particular investigations. Generalizations developed from it have usually resulted in advances in broader fields of pure mathematics. In this book the authors endeavour an elaborate generalization but successfully restrict themselves to the selected field. ... The major contribution is the introduction of general complex vector coordinates for the spheroid such that a direct cartographic transformation can be stated and such that methods of complex function theory can be applied. As a treatment of cartography there is an unexpected but beneficial lack of reference to specific map projections. The analysis rests on the properties of three basic complex vector surface coordinates for the spheroid.

*Gewöhnliche Differentialgleichungen*Ⓣ (1948) in which he discusses Legendre, Bessel, and Sturm-Liouville equations. Also mentioned are existence theorems as well as solutions by iteration, power series, and numerical methods. In 1951, he published his lecture notes on

*Analytical Mechanics*. In 1966 he published, as volume XVII of

*Studia Mathematica*, the monograph

*Differentialgleichungen*Ⓣ. A reviewer writes:-

Weise acted as supervisor of PhD students from a wide range of mathematical fields, a dozen of them went on to become professors, among them Wolfgang Gaschütz (finite groups), Wolfgang Haken (knot theory and the solution of the four-colour-problem), Wilhelm Klingenberg (differential geometry) and Jens Mennicke (topology). Let us look in a little more detail at Weise's influence on one of these students, Wolfgang Haken, who studied mathematics, physics and philosophy at the University of Kiel. Haken attended Heinrich Heesch's talk on his contributions to the Four Colour Problem, but he was most enthused by Weise's lectures on topology. In these lectures, Weise described three long-standing unsolved problems - the Poincaré Conjecture, the Four Colour Problem, and a problem on knot theory. Haken decided to attempt to solve all three problems and began this challenge while studying for a doctorate at Kiel with Weise as his thesis advisor. His thesis, submitted in 1953, wasA student will actually learn everything about this theory which is essential. The treatment is elegant, the text is easy to understand, and carefully written.

*Ein topologischer Satz über die Einbettung (d-1)-dimensionaler Mannigfaltigkeiten in d-dimensionale Mannigfaltigkeiten*Ⓣ. He had solved the knot theory problem and this led to his appointment at the University of Illinois in the United States. Eventually, assisted by Kenneth Appel, he solved the Four Colour Problem in 1976 with the aid of computer techniques.

Weise was retired on 30 September1977, and in the following year the Christian Albrechts Universität conferred on him the title of 'Ehrensenator' (honorary senator).

**Article by:** *J J O'Connor* and *E F Robertson*

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